A Quote “Teachers spend much more time worrying about what they are going to tell students than thinking about what experiences they are going to provide.

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Presentation transcript:

A Quote “Teachers spend much more time worrying about what they are going to tell students than thinking about what experiences they are going to provide for students. To ensure that students learn in class requires carefully designed experiences that keep them engaged and make them think” Weisman © Project Maths Development Team

Chief Inspector’s Report Teach for Understanding Mathematical Rigour Students Collaborating Making Connections Challenge Able Students Justify Reasoning © Project Maths Development Team

A Different Type of Lesson 1 Watch the video and try to guess the question I’m going to ask!! © Project Maths Development Team

Guesstimation! Without any calculations, guesstimate how many Post-its are needed to cover all sides of the file cabinet apart from the base? (P.S. you are allowed to get it wrong!!!) © Project Maths Development Team

What information would be useful to know? © Project Maths Development Team

A Different Type of Lesson 7.618cm © Project Maths Development Team

A Different Type of Lesson © Project Maths Development Team

A Hint!! © Project Maths Development Team

Actual Dimensions Height 183cm Width 91 cm Width 91 cm Depth 46 cm © Project Maths Development Team

Do the Math!!! © Project Maths Development Team

Were you right???? © Project Maths Development Team

Were you right ? © Project Maths Development Team

Can you come up with further questions? If the WIDTH of the cabinet was doubled, how many more post-its would be needed? If the HEIGHT of the cabinet was doubled, how many more post-its would be needed? If the DEPTH of the cabinet was doubled, how many more post-its would be needed? How long would it take to cover if it took 40 seconds for every 5 Post-its ? If you had 1,000,000 Post-its, what kind of file cabinet could you cover? © Project Maths Development Team

Teaching this Way  Engaging for students  Covers the Learning Outcome(s). (3.4 Applied Measure)  Accessible to most abilities  “Realistic”  Differentiation: Challenging extension questions © Project Maths Development Team

A Different Type of Lesson 2 © Project Maths Development Team

Challenge 1 © Project Maths Development Team

Challenge 1 © Project Maths Development Team

Challenge 2 © Project Maths Development Team

Method © Project Maths Development Team

Method © Project Maths Development Team

Method 3 © Project Maths Development Team

Method 3 © Project Maths Development Team

Student Misconception © Project Maths Development Team

Class Investigation © Project Maths Development Team

Possible Areas © Project Maths Development Team

Searching for Patterns: Regular Squares Square1234…………….n Area14916 ……………. © Project Maths Development Team

Searching for Patterns: “1-up” Tilted Squares Square1234…………….n Area ……………. © Project Maths Development Team

Your Turn: “2-up” Tilted Squares Square1234…………….n Area ……………. Square1234…………….n Area …………… © Project Maths Development Team

Searching for Patterns Square1234…………….n Regular14916 ……………. 1-Up ……………. 2-Up ……………. 3-Up ……………. 4-Up ……………. © Project Maths Development Team

Proof: Area of a Tilted Square © Project Maths Development Team

Extension Question © Project Maths Development Team

Further Investigation © Project Maths Development Team

Further Investigation © Project Maths Development Team

Further Investigation © Project Maths Development Team

Further Investigation 1 © Project Maths Development Team

Further Investigation 2 © Project Maths Development Team

Extension 1: Pushing Brighter Students © Project Maths Development Team

Extension 1: Pushing Brighter Students © Project Maths Development Team

Extension 2: Pushing Brighter Students 1. Can you prove that numbers of the form 4n+3 are not possible areas of tilted squares? 2. When is a number expressible as the sum of two squares? © Project Maths Development Team

Content  Slopes of Perpendicular and Parallel lines  Pythagoras’s Theorem  Area of Squares and Right Angled Triangles  Finding areas by “dissection” methods  Surds/ Number Theory  Investigating and Collecting Data  Searching for Patterns  Generalising to a method  Proof  Reasoning, Problem Solving, Persevering. © Project Maths Development Team

Teaching this Way  Connects to other areas of the syllabus  Similar to doing “real” mathematics  Can be adapted to all levels  Level Playing Pitch (entry point is accessible for all)  Enjoyable for Students/Teacher as “guide on the side”  Preparation for exams e.g. Jigsaw question © Project Maths Development Team